content: package Greedy;
  
   /*
   * write a code in java with comments foor As a first example, 
   * we consider a problem where we are given a set of coins and our task is to 
   * form a sum of money n using the coins. The values of the coins are coins = {c1, c2,..., ck}, 
   * and each coin can be used as many times we want. What is the minimum number of coins needed? 
   * For example, if the coins are the euro coins (in cents) {1,2,5,10,20,50,100,200} and n = 520,
   *  we need at least four coins. The optimal solution is to select coins 200 + 200 + 100 + 20 whose sum is 520
   */
  import java.util.Arrays;
  
  public class CoinChange {
  
      /**
       * This method finds the minimum number of coins required to make change for a given amount of money using a given set of coins.
       *
       *  coins The set of coins that can be used to make change.
       *  n The amount of money to make change for.
       * @return The minimum number of coins required to make change for n.
       */
      public static int minCoins(int[] coins, int n) {
          // Create an array to store the minimum number of coins required to make change for each amount of money.
          int[] dp = new int[n + 1];
  
          // Initialize the array to Integer.MAX_VALUE. This means that we do not know the minimum number of coins required to make change for any amount of money yet.
          Arrays.fill(dp, Integer.MAX_VALUE);
  
          // Set the minimum number of coins required to make change for 0 to 0.
          dp[0] = 0;
  
          // Iterate over the coins array.
          for (int i = 0; i < coins.length; i++) {
              // Iterate over the dp array.
              for (int j = coins[i]; j <= n; j++) {
                  // Update the dp[j] element to be the minimum of dp[j] and dp[j - coins[i]] + 1.
                  dp[j] = Math.min(dp[j], dp[j - coins[i]] + 1);
              }
          }
  
          // Return the minimum number of coins required to make change for n.
          return dp[n];
      }
  
      public static void main(String[] args) {
          // Create a set of coins.
          int[] coins = {1, 2, 5, 10, 20, 50, 100, 200};
  
          // The amount of money to make change for.
          int n = 520;
  
          // Find the minimum number of coins required to make change for n.
          int minCoins = minCoins(coins, n);
  
          // Print the minimum number of coins.
          System.out.println("The minimum number of coins required to make change for " + n + " cents is " + minCoins);
      }
  }
  
  // The minimum number of coins required to make change for 520 cents is 4
  